Currently I'm working on 3 projects, and since I've all 3 finished them sompositing in After Effects, but I've got a majure export failliure every time I try to render it out.
I tried several formats, with no difference; every time I start rendering, after about 500-1500 frames (depends on the amount of effects used), it just stops rendering instantly, and when you just klick on a random place or button in the screen, it doesn't respond; it crashed.

Please provide more information. What computer? How much RAM? Output format? Resolution? Source footage? It sure suffocates due to running out of RAM or encountering a "bad" frame in the source files, but without more details it is not possible to provide a solution. In any case, please try some of the suggestions on this site:

You can contact Adobe Technical Support for help with issues like this. You are entitled to a certain number of free calls for "installation issues, basic usage questions, and troubleshooting unexpected behavior for documented features".

For information on what free technical support you're entitled to, see this page:

because as you described that it happens in CS3 and CS4 for me it sounds like a corrupted effect or plugin... did you moved/copied any 3rd party plugins or effects or effect presets from CS3 to CS4?
most former (CS3) compatible 3rd Party Plugins sometime need an update to run properly on never versions of AE. Take a look at the vendors site for updates.

do you have multiprocessing activated?

if any further troubleshooting does not help try deinstalling all recently added codecs or decoder (like Xvid, ffmpegx, DivX) also take care of Perian component if installed.

another solution is to take a look at quicktime settings where you can activate/deactivate legacy codecs. try that.

AVIs with MPEG2 encoding? What is the source of these files? It's quite possible that AE is performing extra conform operations on them and then you run out on disk space for the Media Cache and temporary files. The format being so specific would also be a good explanation for any other crashes...